Kinematics for Bodies Undergoing Residual Stress and its Applications to the Left Ventricle

Abstract

Biological soft tissues are understood to be materials that are residually stressed and nonlinear, and finitely deformed. A generalized continuum kinematics is needed to analyze such materials. Here, we apply Riemann geometry to the analysis of the residual stress and the stress distributions under loading conditions in the left ventricular wall assuming the uniform strain hypothesis. The hypothesis we employ states that the strain is uniformly distributed through the wall thickness at the end diastole. In conventional analyses, in contrast, it has been implicitly assumed that an unloading state gives a stress-free configuration. The steep stress distributions obtained from the conventional assumption are considerably reduced in the present study due to our hypothesis. The results are physiologically more plausible.